This article characterizes new boundary points on the capacity region of certain classes of more capable broadcast channels (BC) with uni-directional cooperation from the stronger to the weaker receiver. The new boundary points are achieved by a simple coding scheme that employs superposition coding at the transmitter with decode and forward at the stronger receiver. We evaluate our general result for Gaussian BCs and for a BC consisting of a binary erasure channel (BEC) to the stronger receiver and a binary symmetric channel (BSC) to the weaker receiver.